The core mass of galaxy clusters is both an important anchor of the radial mass distribution profile and probe of structure formation. With thousands of strong lensing galaxy clusters being discovered by current and upcoming surveys, timely, efficient, and accurate core mass estimates are needed. We assess the results of two efficient methods to estimate the core mass of strong lensing clusters: the mass enclosed by the Einstein radius ($M_{corr}(<theta_E)$ where $theta_{rm E}$ is approximated from arc positions; Remolina Gonz{a}lez et al. 2020), and single-halo lens model ($M_{rm{SHM}}(<rm{e}theta_{rm{E}})$; Remolina Gonz{a}lez et al. 2021), against measurements from publicly available detailed lens models ($M_{rm{DLM}}$) of the same clusters. We use data from the Sloan Giant Arc Survey, the Reionization Lensing Cluster Survey, the Hubble Frontier Fields, and the Cluster Lensing and Supernova Survey with Hubble. We find a scatter of $18.3%$ ($8.4%$) with a bias of $-7.5%$ ($0.4%$) between $M_{corr}(<theta_E)$ ($M_{rm{SHM}}(<rm{e}theta_{rm{E}})$) and $M_{rm{DLM}}$. Last, we compare the statistical uncertainties measured in this work to those from simulations. This work demonstrates the successful application of these methods to observational data. As the effort to efficiently model the mass distribution of strong lensing galaxy clusters continues, we need fast, reliable methods to advance the field.
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